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Equation of common tangent touching the circle (x-3) 2 +y 2 =9 and parabola y 2 =4x above the x-axis is

Equation of common tangent touching the circle (x-3)2+y2=9 and parabola y2=4x above the x-axis is

Grade:12

1 Answers

Arun
25763 Points
one year ago
 

Center of circle: (3,0)

Equation of tangent on parabola:

y=mx+a/m

a=1

y=mx+1/m

Perpendicular Distance from the center of the circle = 3

|3m+1/m|/(1+m)1/2=3

m2=1/3 => m=+1/√3 or -1/√3

As tangent is above x-axis, slope is (+)ve

Therefore, Equation of tangent:

y=x/√3+√3
=> √3y=x+3

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